Statistical Tests Overview

Tests of Means (Comparing Averages)

• 1. One-Sample t-Test - Tests whether the mean of a single sample differs from a known or hypothesized population mean.
• 2. Independent Samples t-Test (Two-Sample t-Test) - Compares means between two independent groups (e.g., treatment vs. control).
• 3. Paired Samples t-Test (Dependent t-Test) - Compares means from the same group at two different times (e.g., before vs. after treatment).
• 4. One-Way ANOVA (Analysis of Variance) - Tests whether three or more independent groups have different means.
• 5. Repeated Measures ANOVA - Tests differences in means when the same subjects are measured under multiple conditions or times.
• 6. Two-Way ANOVA - Tests the effect of two independent factors on a dependent variable, including their interaction.
• 7. F-statistic

Tests of Relationships and Associations

• 1. Pearson Correlation (r) - Measures the strength and direction of a linear relationship between two continuous variables.
• 2. Spearman Rank Correlation (ρ) - Nonparametric version of correlation; measures monotonic relationships using ranked data.
• 3. Chi-Square Test of Independence - Tests whether two categorical variables are related (e.g., gender vs. voting preference).
• 4. Chi-Square Goodness-of-Fit Test - Tests whether observed frequencies match expected frequencies (e.g., dice fairness).
• 5. Fisher’s Exact Test - Used instead of Chi-square when sample sizes are small; tests association between two categorical variables.
• 6. McNemar’s Test - Tests changes in paired categorical data (e.g., pre/post yes-no responses).

Tests of Regression and Prediction

• 1. Simple Linear Regression - Models the relationship between one independent (predictor) and one dependent (outcome) variable.
• 2. Multiple Linear Regression - Extends simple regression to include two or more predictors.
• 3. Logistic Regression - Predicts a binary outcome (e.g., success/failure) from one or more predictors.
• 4. Ordinal Logistic Regression - Predicts an ordered categorical outcome (e.g., satisfaction level).
• 5. Cox Proportional Hazards Model - Tests the effect of predictors on time-to-event data (common in survival analysis).

Nonparametric (Distribution-Free) Tests

• 1. Mann–Whitney U Test (Wilcoxon Rank-Sum) - Nonparametric alternative to the independent t-test; compares medians between two independent groups.
• 2. Wilcoxon Signed-Rank Test - Nonparametric version of the paired t-test; compares median differences within paired data.
• 3. Kruskal–Wallis Test - Nonparametric alternative to one-way ANOVA; compares medians among three or more groups.
• 4. Friedman Test - Nonparametric alternative to repeated measures ANOVA; compares ranks across repeated conditions.

Tests for Variance and Distribution

• 1. Levene’s Test - Tests whether variances are equal across groups (homogeneity of variance).
• 2. Bartlett’s Test - Also tests equality of variances; more sensitive to non-normal data.
• 3. Shapiro–Wilk Test - Tests whether data are normally distributed (goodness-of-fit to normality).
• 4. Kolmogorov–Smirnov (K–S) Test - Compares a sample’s distribution to a reference distribution or compares two distributions.